Artificial impedance surface antennas (AISAs) are realized by launching a surface wave across an artificial impedance surface (AIS), whose impedance is spatially modulated across the AIS according a function that matches the phase fronts between the surface wave on the AIS and the desired far-field radiation pattern.
In previous work described in references [1]-[6] below, artificial impedance surface antennas (AISA) are formed from modulated artificial impedance surfaces (AIS). Patel in reference [1] describes a scalar AISA using an endfire-flare-fed one-dimensional, spatially-modulated AIS consisting of a linear array of metallic strips on a grounded dielectric. Sievenpiper, Colburn and Fong in references [2]-[4] describe scalar and tensor AISAs on both flat and curved surfaces using waveguide- or dipole-fed, two-dimensional, spatially-modulated AISs consisting of a grounded dielectric topped with a grid of metallic patches. Gregoire in references [5]-[6] examined the dependence of AISA operation on the AISA's design properties.
The basic principle of AISA operation is to use the grid momentum of the modulated AIS to match the wavevector of an excited surface-wave (SW) front to a desired plane wave. In the one-dimensional case, this can be expressed asksw=ko sin θo−kp  (1)
where ko is the radiation's free-space wavenumber at the design frequency, θo is the angle of the desired radiation with respect to the AIS normal, kp=2π/p is the AIS grid momentum where p is the AIS modulation period, and ksw=noko is the surface wave's wavenumber, where no is the surface wave's refractive index averaged over the AIS modulation. The surface wave (SW) impedance is typically chosen to have a pattern that modulates the SW impedance sinusoidally along the SW grid according toZ(x)=X+M cos(2πx/p)  (2)
where p is the period of the modulation, X is the mean impedance, and M is the modulation amplitude. X, M and p are chosen such that the angle of the radiation θ in the x-z plane with respect to the z axis is determined byθ=sin−1(n0−λ0/p)  (3)
where n0 is the mean SW index, and λ0 is the free-space wavelength of radiation. n0 is related to Z(x) by
                              n          0                =                                            1              p                        ⁢                                          ∫                0                p                            ⁢                                                                    1                    +                                                                  Z                        ⁡                                                  (                          x                          )                                                                    2                                                                      ⁢                                  ⅆ                  x                                                              ≈                                                    1                +                                  X                  2                                                      .                                              (        4        )            
The AISA impedance modulation of Eqn. (2) can be generalized for an AISA of any shape asZ=({right arrow over (r)})X+M cos(konor−{right arrow over (k)}o□{right arrow over (r)})  (5)
where {right arrow over (k)}o is the desired radiation wave vector, {right arrow over (r)} is the three-dimensional position vector of the AIS, and r is the distance along the AIS from the surface-wave source to {right arrow over (r)} along a geodesic on the AIS surface. This expression can be used to determine the index modulation for an AISA of any geometry, flat, cylindrical, spherical, or any arbitrary shape. In some cases, determining the value of r is geometrically complex. For a flat AISA, it is simply r=√{square root over (x2+y2)}.
For a flat AISA (in the x-y plane), the radiation wavevector be assumed to radiate into the x-z plane {right arrow over (k)}o=ko(sin θo{circumflex over (x)}+cos θo {circumflex over (z)}) without loss of generality. Let the surface-wave source be located at x=y=0. Then, the modulation function isZ(x,y)=X+M cos γ  (6)where γ≡ko(noρ−x sin θ0)  (7)and ρ=√{square root over (x2+y2)}. The cos function in Eqns. (2), (5) and (6) can be replaced with any periodic function and the AISA will still operate as designed, but the properties of the radiation side lobes, bandwidth and beam squint will be affected.
The AIS can be realized as a grid of metallic patches on a grounded dielectric. The desired index modulation is produced by varying the size of the patches according to a function that correlates the patch size to the surface wave index. The correlation between index and patch size can be determined using simulations, calculation and/or measurement techniques. For example, Colburn in reference [3] and Fong in reference [4] use a combination of HFSS unit-cell eigenvalue simulations and near field measurements of test boards to determine their correlation function. Fast approximate methods presented by Luukkonen in reference [7] can also be used to calculate the correlation. However, empirical correction factors are often applied to these methods. In many regimes, these methods agree very well with HFSS eigenvalue simulations and near-field measurements. They break down when the patch size is large compared to the substrate thickness, or when the surface-wave phase shift per unit cell approaches 180°.
Circularly-Polarized AIS Antennas Using Modulated Tensor-Impedance
An AIS antenna can be made to operate with circularly-polarized (CP) radiation by using a modulated tensor-impedance surface whose impedance properties are anisotropic. Mathematically, the impedance is described at every point on the AIS by a tensor. In a generalization of the modulation function of equation (6) for the linear-polarized AISA as described in reference [4], the impedance tensor of the CP AISA may have a form like
                              Z          =                      [                                                                                X                    -                                          M                      ⁢                                                                                          ⁢                      cos                      ⁢                                                                                          ⁢                      ϕ                      ⁢                                                                                          ⁢                      cos                      ⁢                                                                                          ⁢                      γ                                                                                                                                  1                      2                                        ⁢                    M                    ⁢                                                                                  ⁢                                          sin                      ⁡                                              (                                                  γ                          -                          ϕ                                                )                                                                                                                                                                                    1                      2                                        ⁢                    M                    ⁢                                                                                  ⁢                                          sin                      ⁡                                              (                                                  γ                          -                          ϕ                                                )                                                                                                                                  X                    +                                          M                      ⁢                                                                                          ⁢                      sin                      ⁢                                                                                          ⁢                      ϕsin                      ⁢                                                                                          ⁢                      γ                                                                                            ]                          ;                            (        8        )            where φ≡tan−1(y/x).  (9)
In reference [4], the tensor impedance is realized with anisotropic metallic patches on a grounded dielectric substrate. The patches are squares of various sizes with a slice through the center of them. By varying the size of the patches and the angle of the slice through them, the desired tensor impedance of equation (8) can be created across the entire AIS. Other types of tensor impedance elements besides these sliced patches can be used to create the tensor AIS.
All-Dielectric AIS Antennas
All-dielectric AIS antennas have been demonstrated for linearly-polarized operation and described in reference [9]. Dielectric AIS antennas operate according to the same principle of the prior art AIS antennas described above except that the impedance is modulated by varying the thickness of the dielectric.
Scalar-Impedance, Circularly-Polarized, AIS Antennas Radiating at θ=0°
Circularly-polarized (CP) AIS antennas that radiate at θ=0° can be made with a modulated scalar impedance, as described in reference [8]. The impedance is modulated according toZ(x,y)=X+M cos(γ±φ)  (10)
where γ and φ have been defined in equations (7) and (9) respectively, and the ± sign corresponds to an antenna operating in right-hand CP (RHCP) or left-hand CP (LHCP) modes respectively. In appearance, the modulation looks like intertwined, circular spiral lines of constant impedance, such as lines 50 and 52 of low and high impedance, respectively, as shown in FIGS. 2A and 2B. Such an antenna will radiate in a beam perpendicular to the surface of the AIS (θ=0°), as shown in FIG. 2C.
Minatti and Maci in reference [8] deduced the impedance modulation of equation (10) through purely intuitive methods; however, they were unable to generalize it for an antenna radiating at an arbitrary angle.